Question

WILL GIVE BRAINLIEST, 5/5 RATING, AND FAVORITE.

Answer 1

Answer:

$y = -\frac{1}{2}x + 2$

Step-by-step explanation:

Assume this is function is a straight line, consider the equation of the straight line: $y=mx + c$

To find the gradient of the equation, we use any two coordinates from the table. $(x_1,y_1) = (6,-1)\\(x_2,y_2) =(2,1)$

$m = \frac{y_1 - y_2}{x_1 - x_2}\\\\m = \frac{1-(-1)}{2-6}\\\\m=\frac{2}{-4} \\\\m=- \frac{1}{2}$

We substitute the value of m in the equation:

$y =mx+c\\y = - \frac{1}{2} x + c$

To find c, we use the leftover coordinates, (4,0) in the equation above:

$y = -\frac{1}{2}x+c\\\\0 = -\frac{1}{2} \times 4+c\\\\0 = -2 + c\\\\c=2$

Substitute this value of c in the equation to get the function:

$y = -\frac{1}{2}x + 2$